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Simplifying 4x3 + -3x2 + -40x = 0 Reorder the terms: -40x + -3x2 + 4x3 = 0 Solving -40x + -3x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-40 + -3x + 4x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-40 + -3x + 4x2)' equal to zero and attempt to solve: Simplifying -40 + -3x + 4x2 = 0 Solving -40 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10 + -0.75x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -0.75x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -0.75x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -0.75x + x2 = 0 + 10 -0.75x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -0.75x + x2 = 10 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 10 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 10 + 0.140625 Combine like terms: 10 + 0.140625 = 10.140625 0.140625 + -0.75x + x2 = 10.140625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 10.140625 Calculate the square root of the right side: 3.184434801 Break this problem into two subproblems by setting (x + -0.375) equal to 3.184434801 and -3.184434801.Subproblem 1
x + -0.375 = 3.184434801 Simplifying x + -0.375 = 3.184434801 Reorder the terms: -0.375 + x = 3.184434801 Solving -0.375 + x = 3.184434801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 3.184434801 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 3.184434801 + 0.375 x = 3.184434801 + 0.375 Combine like terms: 3.184434801 + 0.375 = 3.559434801 x = 3.559434801 Simplifying x = 3.559434801Subproblem 2
x + -0.375 = -3.184434801 Simplifying x + -0.375 = -3.184434801 Reorder the terms: -0.375 + x = -3.184434801 Solving -0.375 + x = -3.184434801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -3.184434801 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -3.184434801 + 0.375 x = -3.184434801 + 0.375 Combine like terms: -3.184434801 + 0.375 = -2.809434801 x = -2.809434801 Simplifying x = -2.809434801Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.559434801, -2.809434801}Solution
x = {0, 3.559434801, -2.809434801}
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